Relative Performance of Model Selection Criteria for Cox Proportional Hazards Regression Based on Kullback’s Symmetric Divergence

The Cox proportional hazards model is one of the most used models to analyze time-to-event outcomes. The decision on the most suitable model for those data is an essential analysis point. For this purpose, different model selection criteria can be used under various assumptions. This study assesses the relative performance of new model selection criteria based on Kullback’s symmetric divergence in the Cox proportional hazards model. For this purpose, we compared the Kullback information criterion (KIC) and the corrected KICKICc with other information criteria such as the Akaike information criterion AIC, corrected AICAICc, and Bayesian information criterion BIC using a Monte Carlo experiment. Simulations were run using scenarios resulting from the combination of sample size n=30,50,100,200,300, censoring percentage C=5%,10%,15%,20%,25%,and 30%, and censoring distribution (uniform or exponential). The results revealed that the KIC family criteria favor models with more accurate predictive power, irrespective of sample size or censoring percentage. However, they tend to select more underfitted models, which means that the KIC family favors parsimonious models, regardless of sample size or censoring percentage. A larger sample size n=200,300 improves the performance of these criteria in choosing the true model, irrespective of the censoring percentage. However, AIC and AICc outperform the KIC family criteria for relatively small to moderate sample sizes n=30,50,100 in true model (containing only the relevant covariates) selection. In addition, BIC tends to favor underfitted models over KIC family criteria. Variations in censoring percentage, sample size, and censoring distribution affect the performance of these criteria in identifying the true model. These findings suggest that we should prefer KIC or KICc for larger sample sizes and when prioritizing the predictive accuracy of the model. For smaller sample sizes, we should prefer AIC or AICc, and BIC in scenarios where model parsimony is critical. It is important to note that no model selection criterion is the best in all situations, as they performed differently under different circumstances.